[sdiy] Tuning accuracy was: Consider this DAC

[cheater cheater]

Tom,

On Sat, Mar 13, 2010 at 20:36, Tom Wiltshire <tom at electricdruid.net> wrote:
> Cheater,
>
> I notice you're *not* offering an alternative definition of  "good enough".

No, I leave that as an open-ended question. I indicated some
directions to explore in the email, but an answer is enough of a topic
for a bachelor's or even master's / phd thesis.

> Simon had a crack, and you and Antti have both provided a reasonable case
> for why 2.5 cents isn't close enough. I concur, it isn't.
>
> So what are you offering? What's *your* best guess? Better still, what have
> you practically demonstrated to be sufficient for your needs?

I have practically demonstrated that 0 deviation is sufficient for my
needs by using VST plugins. I have not experimented on how badly it
can get detuned before I start having problems making music.

> I'm always looking for other people who've made their own judgements about
> this kind of stuff, because it seems to me that there is a lot of compromise
> in synth building (indeed, engineering in general) and that making the right
> compromises in the right places is one of the things that separates the
> great instruments from the good ones.

Yes, and when making compromise you need to know what the musicians
using your synthesizer will actually find useful.

But there's more to that.

Sometimes a difference of 50% which costs you 150% the money in
work/materials is not worth it. For example, whether the tuning will
be +- 5 or +-7 Hz accurate doesn't make a difference. And you can go
on improving it a long way and it won't make a difference, until it
gets to the region of 0.25 Hz at which point it starts making sense
again; sometimes an optimization in performance is pointless not
because it's too much, but because it's too little.

> I find that failure to compromise
> effectively on a design leads to failure to actually get the thing done,
> since you finish up wasting time chasing some unrealistic goal or other.
> Better to choose 2.5 cents and get it running and be proved wrong than
> decide 0.1 cents is what it must achieve and never hear it to know.

But 2.5 cents is not unseen performance - there are 100s of synths
that do this - I've "seen it" too often by now - it always sounded
pretty crap - that's why barely anyone records full albums on analogue
synths, except for very minimal approaches to harmony. Listen to any
80s synth albums and most of them except for the best sound bad
exactly because of instruments that don't tune.

I've also heard 0.1 cents and better (just try any good VST plugin, I
suggest fxpansion synth squad) and can validate its utility.

So why build new synths that don't learn from the errors of the old synths?

> For what it's worth, the Roland Juno 106 gets by with a worst-case pitch
> error of 1.4 cents. That's not the pitch resolution, necessarily, just the
> amount it deviates from the notes of the equally-tempered scale. Most of the
> range is much better than that (<0.5cent). The DCO is only a 16-bit counter,
> so no-one remarks on it's amazing DCO smoothness (unsurprisingly), but at
> the same time, lots of people still find it a useful synth. It constantly
> amazes me what you can get away with!

You're mistaking things. An alternate tuning is not the same thing as
lack of pitch accuracy. In its own tuning, the 106 is going to be very
very accurate (wonder *how* accurate, actually - anyone know what
jitter the 106 counter has?)

And further to that, all its voices are kinda sorta hard synced, which
from the point of view of harmony means it works in compositions as if
it were a single voice.

> The whole question became a moot point for me as soon as I started basing
> everything on a 32-bit NCO. Instant frequency accuracy up the wazoo!

There you go - now you can make your own tests of 0.1 cent pitch
accuracy. :) When does it stop working for *you*?

I think pitch accuracy should be counted in Hz and not in cents; I
don't see a reason why it should be counted in cents since the beating
resulting from pitch inaccuracy depends on the frequency difference in
Hz, and not on the musical pitch interval.

D.

> On 13 Mar 2010, at 14:58, cheater cheater wrote:
>
>>
>> Simon, I am impressed with your technical knowledge of digital
>> electronics. However you still need to study some psychology to talk
>> about pitch perception like that. Throwing around statements like the
>> above, after ripping them out of context, makes for a lot of
>> disinformation and establishes very destructive myths.
>>
>> What you have brought up is the experimentally established 'just
>> noticable difference' threshold. Just noticable difference, even
>> though it sounds like regular english, is a specific term in
>> psychology; it is bemoanable, but outside of the scope of this
>> discussion, that names for such concepts are constructed in a way that
>> allows people to use them without knowing that they are, in fact,
>> "sharp" - or, simpler said, exact - scientific definitions.
>>
>> Without knowing what sort of experiment and situation the sample data
>> actually reflects, it is in no way intelligible.
>>
>> You can skip the next paragraphs until the -------- line, unless
>> you're interested in what a JND actually is.
>>
>> The definition of the JND can be put into words as such: first we
>> expose someone to a stimulus, for example showing a light of a certain
>> length. Then after the stimulus is over another one, slightly
>> different, is created in the same way. The two stimuli are quantified
>> with a single dimension, and assigned a single number. So for example
>> a person is exposed to a light source of color 227.1 and then,
>> *later*, of color 227.132. For such pairs of stimuli, a test subject
>> is asked whether they were different or not. For statistical reasons,
>> for each pair which is included in the testing suite, the test is
>> repeated hundreds or thousands of times.
>>
>> Each pair (I1, I2) in the test suite is assigned a difference, this is
>> our Delta I. If across all measurements there is a specific Delta I
>> below which a significant amount of subjects do not notice a
>> differende, but above which they do, then that's the just noticable
>> difference value.
>>
>> (notably, if the JND seems to depend on the base value of I1, then a
>> different scale can sometimes be used; the logarithmic scale of pitch
>> has a more or less constant JND, whereas the linear scale of frequency
>> in Hz has one that rises as I1 rises, that's why the JND for
>> successive perception of tone height is expressed in cents, i.e. the
>> distance on the logarithmic scale)
>> -------------
>>
>> The key word above is *later*. The test subjects are played back a
>> tone at some pitch, and then *later*, after that note is *finished*,
>> they are played a second tone. It is a huge difference from the way we
>> are defining the required accuracy of a musical instrument; to see
>> why, consider this:
>>
>> at 5000 Hz, the difference of 1 cent is almost 3 Hz:
>>
>> 5 000 * 0.000577789 ~= 2.888945
>>
>> Even consider something as small as 0.3 cents:
>>
>>
>> 5 000 * (1.000577789^0.3) = 5 000.86651
>>
>> This gives us a difference of ~0.8 Hz. This means that if I play two
>> notes *at the same time* and they have this difference in pitch, I
>> will be able to hear them pulsate in
>>
>> 1 / (0.86651 Hz) ~= 1.15405477s
>>
>> so about 1.2-second intervals. I don't know about you, but I can hear
>> this sort of thing very clearly. I would say that the JND here is much
>> lower, and should be expressed in Hz; furthermore, it will decrease
>> with the amount of coexisting notes and the note length and increase
>> with the richness of tone, to mention some easy to notice variables in
>> the equation. The test here would look like this: first we play two
>> notes at one pitch difference, then two notes at another pitch
>> difference, and we ask if the subject notices a difference.
>>
>> The speed of vibration between notes is very important in chromatic
>> and generally harmonic compositions.
>>
>> 2.5 cents of inaccuracy can mean a difference between one note slowly
>> and pleasantly pulsating with another note's 3rd harmonic, and it
>> grating at a displeasurable 7 Hz.
>>
>> Your so-called just noticable difference of 2.5 cents can be a
>> catastrophe in musical terms.
>>
>> D.
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